Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Two resistors having equal initial resistance R₀ at a reference temperature, one with a positive temperature coefficient of resistance ( + ) and the other with a negative temperature coefficient ( - ), are connected in parallel. As the temperature of the combination increases, their equivalent resi

Step-by-step solution

Let the resistances at an increased temperature be R₁ = R₀(1 + T) and R₂ = R₀(1 - T) . The sum of the resistances is: R₁ + R₂ = R₀(1 + T) + R₀(1 - T) = 2R₀ This sum is independent of the temperature change. The product of the resistances is: R₁ R₂ = R₀(1 + T) R₀(1 - T) = R₀^2(1 - ^2 T^2) As temperature increases ( T increases), the term (1 - ^2 T^2) decreases, so the product of the resistances decreases. Thus, the Reason (R) is true. The equivalent resistance in parallel is given by: R_ eq = R₁ R₂ R₁ + R₂ = R₀^2(1